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E - Bibliothèque et Archives Canada

E - Bibliothèque et Archives Canada

geornetncal optics ternis it is easy to see that üie incident field is present everywhere exœpt between ISB 1 and ISB 2 below the strip The refîe field is present only behNeen RSB 1 and RSB 2 above the Wip. To evaluate the diffractai field howwer, the strip is considered to be a eination of hm edges (back to back) one at A and the other at B. These edges are half planes (n=2). The difhcted fields from A and 6 can be camputad from equations 2.3 and 2.4. The d*rffraction coefficient parameters must howewr be properly defined. For the case of Figure 2.1 (a). they are: D:~(~~,L~,P,P'.~) and fl&h~,v,y',n) where, pA = distanœ from the observer to A pe = distanœ from the observer to B LA=PA ( plane wave incidence) L~=pe (plane wave incidence) Q'= angle of incident wave with 'O foce' of edge A Q= angle of 3~ with 'O hce' of edge A g'= angle of incident wave with 'O face' of edge B w =angle of 3~ with 'O fa-' of edge B n=2 (half plane) For this case. the strip upper surface was considered to be the 'O face' of edge B but if it was the lower surface to be used, and w' should be repbced by 4 and 4' r e~~vely. The building of more complex geometries cm be done also by considering A and B to be 90" edges (back to back) and add to them anobr lwo 90° eâges C and D below to fom a rectangutar cylinder. The sam analysis f o(ld above applies to the rcdangular cylinder with additional RSBs and ISBs to nspad al1 the surfaces and with diffraction coefficient paraMers evaluateâ with respect to 7

the distance from each edge and the angle from each edge 'O face' surface mth n being representative of the angle of the edge. The above listed UTD formulation was derived using asymptote approximations for high frequencies. It should not be forgotten here that by high frequency approximation, 1 is meant that kL is assurnecl to be large. This means that the observation point is far away from the dge. No deep investigation howaver has shom yet to what extent this fomulation can be used with success when going lower in frequency. In P] it is mentioned that the dimadon coefficient obtained by UT0 for an incident plane wave (L=p) is found to be acairate for kPl .O. In [4], the field enw computed by UTD as dose as 0.25 k near the edge of a 90° wedge was found to be very srnall. The goal of the present work is to show to what extent the fraquency can be reduœd, with the UTD fomiulation still king acairate. Practically speaking this does not imply verifying only the total UTD field solution accuracy near the edge of scattering created by incident plane waves on infinite Mges, it amsists of the following: a) Verifying the accuracy of UTD when used on eIBcfTjcally small scattemrs. Sinœ diffraction is a local phenomenon, the infinite edge canonical solution can be used as a building block solution for different 2-0 shapes scatterers like plates and rectangular cylinders. b) Verifying UTD succcsrr when used to figure the cumnt singularity at the eâge, which exists in the TMz case C) Venfying UTD sucœss Men used on electrically smll scatterers whem the phemnon of multiple diffraction due to nearby dges becornes important. In this case not only incidence of plane waves (at low

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